In my statistics class we learned formulas for the means and variances
of the T and F distributions. I've been trying to derive the formulas
but have not been able to do so. Can you help me get started?

Why is the modal class of a histogram with unequal class widths the
bar with the highest frequency density? I have always been taught that
the modal class is the one with the highest frequency from a histogram
or frequency table. What role does the density play?

I have a set of data points that I have collected from an experiment.
I want to fit a 3D plane (best-fit) into these points (the points are
in the form (x1,y1,z1), (x2,y2,z2),...) in order to evaluate my
results.

80 percent of light bulbs last 2400 hours, 20 percent last 2400 hours...
Given a collection of screws with a Gaussian distribution of size.... The
frequency of a mistake for wires is once in 25 meters...

In error analsysis, sometimes an RMS equation is used and sometimes an
RSS equation is used to calculate overall error given a list of
contributing variables. Can you explain both concepts and the
stipulation of the dependencies between the contributing variables?

If the variance of a probability distribution for a continuous random
variable with a mean of zero can be found by integrating (x-squared
times f(x)) between the end bounds of distribution, and the indefinite
integral is easily obtained, but leads to an infinite value when the
definite integral is calculated, how do you work out the standard
deviation of the Cauchy distribution?

I am doing a lab report comparing two different samples of fish. For
the results the teacher wants a t test. What does the t value and
two-tailed p value tell me and how do they compare to each other? Is
this information 'significant' enough to say that variable 2 came from
the same family as variable 1?

Train cars are loaded with ore. The distribution of ore into the cars
is normally distributed with a mean of 70 tons per car and a standard
deviation of 0.9 tons. What is the probability that the weight of ore
in a randomly selected car will be 70.7 tons or more?

I need help in deriving the variance (n/(n-2)) (n: degrees of freedom)
of the T-Student Distribution. The most difficult thing is how to
apply the VAR to a ratio of a normally distributed variable divided by
a Chi-Square.